I work part-time for an inventory company. We travel to various retail stores to perform inventory audits. A few days ago, I was part of a group of 3 workers plus a supervisor who left in a company van to go to another city to do an inventory. The inventory was scheduled for 5 hours. (We left at 3:30 AM)

Just before we left in the van, the supervisor told us we would have to go onto another job that is not on our schedule and help another team out. I told her I could do this if we were able to be back at the company parking lot at 2:PM becuase I had an important appointment I had to keep that afternoon. She promised me we would return by that time.

After completing our scheduled job, we got to the 2nd job to help out the other team. When the time came for us to leave at the promised time, the same supervisor said we were not leaving until the inventory was completed. We did not return to the company parking lot until after 4 PM. I (and the other 2 workers) were furious with her. Since we had left our cars at the company's parking lot (over an hour away), we were stranded and at the company's mercy. Generally speaking is the supervisor's action legal?

Certainly it is. Obviously the inventory took longer than expected. The employer has no obligation to take your personal appointments into consideration. And even if she did "lie" (which is not necessarily the case), that's not illegal.